(CNN) -- The mayor of Cambridge, Massachusetts, said she is going to meet with the city's police chief to make sure the scenario that caused the arrest of a prominent black Harvard University professor does not happen again.

Harvard University professor Henry Louis Gates Jr. says he and his attorneys are considering further actions.

"This suggests that something happened that should not have happened," Cambridge Mayor E. Denise Simmons said on CNN's "American Morning." "The situation is certainly unfortunate. This can't happen again in Cambridge."

Harvard scholar Henry Louis Gates Jr. was arrested last week at his home after a confrontation with an officer investigating a possible break-in, according to a Cambridge police report.

Obama defended Gates while admitting that he may be "a little biased" because the professor is a friend of his.

"But I think it's fair to say, No. 1, any of us would be pretty angry; No. 2, that the Cambridge police acted stupidly in arresting somebody when there was already proof that they were in their own home; and, No. 3 ... that there's a long history in this country of African-Americans and Latinos being stopped by law enforcement disproportionately." Was the professor profiled? »

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The incident shows "how race remains a factor in this society," Obama said.

Obama's remarks are being questioned by Senate Republicans, whose campaign arm is paying for a Web ad asking whether it is appropriate for the president to say Cambridge police acted stupidly.

The ad will run on the Drudge Report.

"This isn't taking sides between the police officers and Mr. Gates," said Brian Walsh, spokesman for the National Republican Senatorial Committee. "It is the issue of whether it is appropriate for the president of the United States to be weighing in and taking sides before, by his own admission, all the facts are known."

White House Press Secretary Robert Gibbs said Thursday that Obama doesn't regret his comments.

Obama "was not calling the [arresting] officer stupid. The situation got out of hand," Gibbs said.

Gates said on Wednesday that although charges were dropped, he will keep the issue alive.

"This is not about me; this is about the vulnerability of black men in America," Gates told CNN's Soledad O'Brien.

Gates said he'd be prepared to forgive the arresting officer "if he told the truth" about what the scholar called "fabrications" in the police report.

The officer, Sgt. James Crowley, told CNN affiliate WCVB-TV in Boston, Massachusetts, on Wednesday that he will not apologize.

"There are not many certainties in life, but it is for certain that Sgt. Crowley will not be apologizing," he said.

Crowley wrote in the Cambridge police report that Gates refused to step outside to speak with him, the police report said. When Crowley told Gates that he was investigating a possible break-in, Gates opened the front door and exclaimed, "Why, because I'm a black man in America?" the report said.

The report said Gates initially refused to show the officer identification but eventually produced a Harvard identification card, prompting Crowley to radio for Harvard police. Gates is director of Harvard's W.E.B. Du Bois Institute for African and African American Research.

"While I was led to believe that Gates was lawfully in the residence, I was quite surprised and confused with the behavior he exhibited toward me," Crowley said, according to the report. iReport.com: "Shame" on Gates

Gates was arrested for "loud and tumultuous behavior in a public space" and was released from police custody after spending four hours at the police station.

Gates said Wednesday that he and his attorneys were considering further actions, not excluding a lawsuit.

Gates said that although the ordeal had upset him, "I would do the same thing exactly again."

Earlier this week, a prosecutor dropped the charge against Gates and the Police Department recommended the matter not be pursued.